Hussain al-Hilli's final memories of his cousin Saad are of an anxious, desperate man, burdened with a secret that may have taken him to the grave.

Last February, six months before Saad and his family were murdered, the pair were having one of their regular Facebook chats, normally a chance to swap notes on two very different lives. While Saad would bring news from leafy Surrey, Hussain would bring talk of life – and sometimes death – in Baghdad, the war-torn Iraqi capital from which Saad's side of the family had left decades before. This time, though, Hussain noticed something odd straightaway.

"He sounded worried about something, saying he was not feeling OK, and that he wanted to come to live in Iraq," Hussain recalled last week.

"I thought: why would an Iraqi who has lived most of his life in England suddenly want to come to live here, when nearly every other Iraqi would love to come and live in England? I didn't ask him much about it at the time. I wish I had now."

Hussain, 59, never did find out what made his cousin want to leave England.

Six months later, in a crime as violent as anything on the streets of Baghdad, Saad, 50, was gunned down along with his wife Iqbal, 47, and mother-in-law Suhaila, 74, as they holidayed near Lake Annecy in the French Alps. Mr Hilli's daughter, Zainab, seven, was pistol-whipped, shot in the shoulder and left for dead, while Zeena, four, only survived by hiding under her dead mother's skirt. Also shot dead was a French cyclist, Sylvain Mollier, 45, who may have simply stumbled on the crime scene while it was still in progress.

In the absence of any arrests since, the question of what would lie behind such savagery has produced endless speculative theories, many drawn straight from thriller novels.

One is that Mr Hilli was involved in espionage connected to his job as a satellite engineer. A second is that it was a carjacking gone wrong, or the work of a random psychopath. But a third, perhaps inevitably, is that the answers lie back on the violent streets of Iraq – possibly in a dispute over properties owned there by Mr Hilli's father, Kadhim, which Saad had been trying to recover.

Last week, The Sunday Telegraph travelled to Baghdad in a bid to shed light on the Iraqi end of the mystery, where local members of the Hilli family agreed to speak publicly about the murder for the first time. They did so in a bid to set the record straight after recent French newspaper claims that Saad's father, who fled Iraq after falling out with Saddam Hussein, was in fact a secret money launderer for the Iraqi dictator, and that his son knew the whereabouts of millions of dollars salted away in secret bank accounts.

"This is not true," said Hussain, an official with an Iraqi charitable organisation. "The Hilli family were not liked by Saddam, who forced Kadhim to flee and also jailed two other relatives. It is hurtful for us to hear people say that they were laundering money for him."

Like many others, though, Hussain is at a loss to explain what really did happen, and is haunted by Saad's cryptic email to him back in February, details of which have never been revealed until now.

"When the news of the killing broke we were absolutely shocked," said Hussain, whose own father, Ali, was the cousin of Saad's father, Kadhim.

"That kind of murder, with the wife and mother-in-law, and the French witness too, it must be a Mob or an intelligence-style killing?"

One widely-mooted theory, however, is that it was a more domestic dispute, involving Saad's father Kadhim's old home in Baghdad's Adamiyah district, a wealthy district favoured by the Iraqi elite during Saddam Hussein's rule.

Nicknamed Chelsea-on-Tigris, it became a hotbed of the anti-US insurgency after Saddam's downfall, and in the brutal sectarian war that followed, rival Sunni and Shia death squads fought savage turf battles amid its Beverly Hills-style mansions.

Today, nearly 10 years on from Saddam's fall, an uneasy calm prevails, with Iraqi army Humvees patrolling the bomb-devastated streets, and long-shuttered shops and souks reopened. But turn down one bullet-peppered alleyway near the Al Sabah bookshop, and one comes to Kadhim's former house, an unoccupied villa hidden behind palms and metal gates.

It was outside these gates, back in December 2003, that Saad had a violent argument that could easily have cost him his life.

"When Kadhim left Baghdad in 1981, the property was stolen by another family, so after Saddam's fall in 2003, Saad came back to reclaim it," recalled Hussain, who said it was the first time his cousin had returned to Iraq.

"But he went to the house alone, and there was a dispute with the people living there. A woman answered the door and started shouting at him, and then two men started kicking him and punching him. Saad came home bleeding from the head. When I saw him I told him: 'Are you crazy? You should never have gone there alone, you could have got killed.'

"But Saad was a quite a confrontational guy, and he liked to fight for his rights. Later he told me that he had got the house back. When I asked him how, he just said: 'I used some connections.'"

Quite what that meant, Hussain does not know, although in the immediate anarchy of post-Saddam Iraq, such disputes were routinely resolved with hired muscle. Could it, though, have ignited the feud that led to his death?

Certainly, it is true that while property prices in oil-rich Iraq remains high, life remains cheap; similar property disputes claimed the lives of countless of other Iraqis in the aftermath of Saddam's demise. However, with Kadhim's villa worth no more than half a million dollars at most, it seems unlikely that someone would have pursued the debt all the way to France a decade later, let alone settled it in such spectacularly violent fashion.

Besides, another of Saad's Iraqi cousins, Balsam, gives a slightly different version of events. She says that the family in the house were not illegal squatters but a lawyer and his wife, who were actually living there with the Hilli family's permission, and only left when the insurgency in Adamiyah began raging in 2004.

"They may have had an argument with Saad that day, but that was maybe just because they weren't expecting him to suddenly turn up after all these years," she says.

Both Balsam and Hussain also dismiss the theory that the house in Adamiyah was instead part of an inheritance feud between Saad and his older brother Zaid, 53. Saad reportedly put a block on his father's will after he died in Spain last year, halting his brother Zaid's claim to any inheritance.

But Zaid, who also lives in Surrey, has strongly denied any suggestion of a blood feud, and French police have said he is not a suspect. Nor is it known publicly whether the will, which is still sealed, even mentioned the Adamiyah house – Balsam believes it did not.

"I dismiss the family dispute theory because I know that Zaid is a very gentle, peaceful sort of man," added Hussain, who played with the older brother as a child. "If anything, it was Saad who was the tough one."

Likewise, the Iraqi side of the family denies any suggestion that Kadhim was laundering money for Saddam, and that his claim to have fled to England because of persecution was simply a cover-story. They insist that like many other successful Iraqi businessmen, Kadhim, who ran a string of enterprises ranging from a poultry farm to Iraq's first Kleenex factory, left mainly because Saddam and his Ba'athist cronies were extorting much of their profits.

He added that the wider Hilli family were also distrusted by Saddam because they had held senior positions in Iraq's monarchical regime, which the Iraqi despot's Ba'ath party had opposed. Balsam's own father, Hashim, who served as as diplomat, was brutally tortured in jail in 1969, turning him into "a completely different person, terrified of everyone and everything," according to his daughter. Another Hill relative was imprisoned by Saddam's half-brother, Barzan al-Tikriti, who seized shares in his businesses.

"This tells you that the family were not in a good relationship with the regime," said Hussein. "The theory that this was all to with Saddam's money was baseless."

On that question, it would seem Hussein is right. Officials involved in tracking Saddam's hidden millions over the years have told The Sunday Telegraph that Kadhim al-Hilli's name has never come up on lists of known money-launderers, while French prosecutors have also said that the theory is "baseless".

So what do the Iraqi side of Saad's family think really did happen?

Hussain believes the real clues lie not in Iraq, but back in England, where Saad was employed by Guilldford-based Surrey Satellites Technology Limited, a firm involved in map-making technology.

Saad was reportedly working a project linked to European Aeronautic Defence and Space, a pan-European defence giant which has contracts with Russia, China and the Foreign Office.

French and British police have made inquiries at the firm, and while the exact nature of his work for them is not known, the absence of any comment from colleagues – even to point of posting no condolences on a Facebook page set up in Saad's memory – has led many to draw significance from the silence.

The theory goes that Saad, a Shia Muslim who was strongly anti-Israeli and supportive of Iran and their Lebanese militia allies, Hizbollah, might have accessed sensitive technology secrets of use to Israel's enemies.

"We used to discuss politics in our online conversations, and I was surprised by how radical he was – he was very supportive of Palestine, Hizbollah and Iran," said Hussain. "If he tried to give his technology to one of those Middle Eastern powers, he would incur the anger of their rivals. I have no proof of this, but if he was stuck between them, there could be some consequences."

Hussain points the finger at Israel, saying Mossad would not hesitate to wipe out anyone offering to help Tehran, just as they have done with scientists involved in Iran's nuclear programme. Others, though, think that if Saad had been hawking secrets around, it is just as likely that he fell foul of those he was trying to sell them to, either because the deal went sour for some reason, or to silence him afterwards.

Balsam, for her part, thinks that neither espionage theory sounds plausible, and fears that Saad may indeed have been the victim of a random killer. But she adds that even the police seem baffled up until now. "I speak to Saad's brother Zaid sometimes, and it seems that the detectives do not seem to have any leads at all. The fact is we simply do not know. Besides, if Saad was involved in some dangerous business in France, he would hardly take his family with him."

But what about Saad's foreboding Facebook conversations with Hussain earlier this year? Hussain was so taken aback by his cousin's comments that he actually saved them on his computer, and says he is willing to show them to French police in case they shed light on matters.

During some of the conversations, Saad also expressed frustration about having lost various computer passwords and having his Skype account password "stolen". Again, what seemed like petty gripes at the time just might, with hindsight, have significance.

As of yet, though, neither French or British detectives have made contact with either him or Balsam, although earlier this month French prosecutors did send a dossier on the case to their Iraqi counterparts. With killings in Iraq still running at up to 100 a week, though, it seems unlikely that the local police will spare much time for a case that took place 3,000 miles away.

Instead, Hussain fears that his distant cousin's murder may end up like all too many in Iraq itself: tragic, perplexing and ultimately unsolved.

"It's seems like a very complex crime, that will be hard to get to the bottom of," he said, shaking his head. "But if the truth points in a way that is politically uncomfortable for someone, then we will not find out.

"That is why they will say it is a family dispute, or that it was to do with Saddam's money. It will remain a mystery – just like the murder of JFK."